Let's says I have unequal monthly interest rates (1,5% in the first month, 1,7% in the second, -0,8% in the third...) is there a way I can calculate what was my interest rate in the semester or in the year? On all the formulas I could manage to find it is taken into consideration that monthly rates are always the same.
You can use the geometric mean, e.g.
quarterly return = (1 + 0.015)*(1 + 0.017)*(1 - 0.008) - 1 = 2.3997 %
Using the geometric mean
gm = 1.007935842 quarterly return = gm^3 - 1 = 2.3997 %
So the average monthly return is
gm - 1 = 0.7935842 %
The effective annual interest rate would be
gm^12 - 1 = 9.94986 % and the nominal annual rate compounded monthly would be
(gm - 1)*12 = 9.52301 %.